This differs slightly from the Apple Music iMessage app, which lacks a search function completely. If you want to share a specific Apple Music song with a friend, it has to be in your recently listened track list, meaning you'll have to jump to the Apple Music app, search for it, play it, and then navigate back to Messages to find it in the app drawer. Apple Music's big advantage is that you can listen to the full track right in Messages.
The design is also different, with Spotify's iMessage app displaying a larger image for the song's album artwork, while Apple Music's remains thin and more horizontally-aligned with a play button directly in the iMessage.
In recent Spotify news, the company's Web Player is now incompatible with Apple's Safari browser, reportedly due to Google's Widevine media optimizer plugin, which Spotify requires for music streaming on the web and Apple opposes due to potential security issues. Spotify will also debut an official Apple Watch app in the future, although news of that release now dates back to April 2017 and there's since been no other word from Spotify or the app's developer Andrew Chang, besides a few mentions on Reddit over the summer.